Summary

International Symposium on Nonlinear Theory and its Applications

2008

Session Number:C3L-E

Session:

Number:C3L-E3

Detection of regular patterns within randomness

Ruedi Stoop,  Markus Christen,  

pp.-

Publication Date:2008/9/7

Online ISSN:2188-5079

DOI:10.34385/proc.42.C3L-E3

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Summary:
The identification of slightly jittered regular signals (=“patterns”) embedded in strongly noisy background is a nontrivial important task, particularly in the neurosciences. Whereas traditional methods generally fail to capture such signals, staircase-like structures in the log-log correlation plot are reliable indicators. We provide the analytic relationship between the length of the pattern n and the maximal number of steps s(n, m) that are observable at a chosen embedding dimension m. For integer linearly independent patterns, the length of the embedded pattern can be calculated from the number of steps. We, moreover, discuss several applications of this concept that demonstrate the power of this concept.